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Hm. I haven't seen that, but it sounds like maybe the piece is "modal" as we say in traditional music. For instance, if the piece has 2 sharps, which would normally make it D major, but the actual tonal center is A major and the piece has no G sharps, in traditional circles we'd say it's in A Mixolydian. A Mixolydian doesn't have a formal way of marking the key signature, so this might be a way to indicate that.

So check to see if the piece ends on an A major chord, rather than a D major, if it in fact has a "natural" sign in the key signature for G.

At any rate, see if the tonal center is different from what you would expect it to be if the natural sign wasn't there.

I think that Justpin is looking at something different since he says the sharps and flats are written in as accidentals. There are two possibilities. One is where method books try "not to confuse beginner students" by first writing in accidentals before key signatures are introduced. (We've seen examples of that.) The other is where someone has transcribed what was heard by ear or some software did it.

justpin, a scan would help greatly. In the meantime, can you describe more precisely what you're seeing? I understand you to be saying that instead of seeing a standard key signature (sharps or flats only, in a standard configuration) between the clef and the time signature, instead you are seeing some natural signs, plus either some sharp or flat signs, or maybe both?

Is this correct?

If so, what signs exactly are you seeing and on which line or space does each sign appear, in order from left to right?

For example: "treble clef, natural sign on fifth line F, flat on third space C, sharp on space above the staff G" (to make up a hypothetical illustration).

Is this at the beginning of the piece, or someplace in the middle of the piece?